Humber, as far as I can see, there are two problems in this diagram.
1. In the "real world" version at the top, you've shown a part of the boundary layer that is moving at 7 m/s (relative to ground). In the treadmill version you've shown a 7 m/s vector in the same direction as the belt. But to compare apples with apples that 7 m/s vector needs to be 3 m/s (which actually makes it 7 m/s relative to the belt), because it "nearer the top of the boundary layer than the bottom" if that makes sense!
2. You've then tried to calculate the velocity of that part of the boundary layer relative to the cart. That's done correctly in the "real world" diagram, but in the treadmill version you have another mistake. To get the velocity of the boundary layer relative to the cart, you need to subtract the cart velocity from the boundary layer velocity. You've done that part wrong. If A and B are vectors (say drawn on paper), then to subtract B from A, you need to reverse the direction of B and then add that to A (adding by connecting the arrow on A to the tail of the reverse B). So to see the direction of the boundary layer on the treadmill relative to the cart you need to subtract the cart vector (0 m/s) from the boundary layer vector (which should really be 3 m/s to the left) and that will give you 3 m/s to the left which is the same as the real world version.
Hope this makes sense (and that I've interpreted your diagram and intentions correctly).
ETA: Belatedly I see now that mender already covered a lot of this (and mentioned it below also). I'm clearly far too slow (and error prone)!
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